Editor’s Note: Out this month is Lib Dem MP Jo Swinson’s book Equal Power. Here she writes about the battle for equality and you can get her new book yourself from Amazon, Hive or The Guardian bookshop.

With rampant sexual harassment at a corporate charity dinner, the BBC accused of breaking equal pay law, and Easyjet’s new male CEO admitting he was offered £34,000 more to do the same job as his female predecessor, you don’t need to look far to find gender inequality in the news. And that’s just stories from one week.

When I was the Liberal Democrat Minister for Women, I learned that many seemingly different issues – the gender pay gap, violence against women, workplace discrimination, body image, division of caring responsibilities, gender stereotypes, women’s under-representation in politics – are all different parts of the same fiendishly difficult jigsaw. Tackling the problem of gender inequality means chipping away at all of these issues simultaneously because together they reinforce the entrenched power imbalance between men and women.

The backlash in the letters page of the Financial Times last week showed what we’re up against, as writers bemoaned the FT even covering the issue of sexual harassment, and referred to the women groped in their workplace as “silly young girls”. When I spoke out on television – albeit colourfully – against the everyday sexism and misogyny that sees schoolgirls sexually harassed, I was called a “little missy”.

It should be a core mission for us as liberals to challenge concentrations of power, including the power hoarded in the hands of rich, white men.

Gendered assumptions are everywhere. While women bear the brunt of these injustices, rigid cultural expectations about gender also harm men, not least in terms of their mental health. Men are also undervalued in their role as fathers, something I started trying to change with the introduction of shared parental leave.

Our party is not immune to the sexism that permeates through every part of society, but we can all act – individually and collectively – to be part of the solution. We need to recognise the nature of the problem: it is structural and ingrained in each and every one of us, absorbed from the surrounding culture. Changing it takes constant attention and proactive effort. Wringing our hands or shrugging our shoulders when few women ‘come forward’ won’t cut it for our party in 2018.

Talking about periods apparently is still taboo. In fact we have had to wait until this month, in 2017 for the first ad ever in the UK to show a hand pouring a test-tube of blood-coloured liquid onto a sanitary towel, in lieu of the standard sterile-blue.

The advert, which forms part of a new campaign called ‘Blood Normal’, attempts to get rid of the embarrassment around the ‘Aunt Flo’ after a recent survey found that nine out of ten women attempt to hide the fact they are on their period, and 56% of girls said they would rather be bullied at school than talk to their parents about periods.

For something half the population experience on a monthly basis that is ludicrous.

For the majority of us they are an inconvenience, for example feeling we have to take our entire handbag with us to the bathroom at work, the surest tell-tale sign. But for others, particularly girls who have just started menstruating, the embarrassment can be enormous resulting in lost days of schooling and a huge knock to their self-esteem. This is particularly the case for girls from low-income families who might see their parents struggling to make ends meet and feel reluctant to ask them to add sanitary products to the weekly shop.

A survey by Plan International UK found that 1 in 10 girls had been unable to afford sanitary products. The fact that no one talks about this means that it remains hidden. In a country as well-off as Britain this simply shouldn’t be happening. And it can be stopped. We can end period poverty. The truth is it, it wouldn’t even cost a lot, relatively speaking.

It feels like an age since I was knocking on doors in the pouring rain in the final hour before polls closed, then hearing the shock of the exit poll on the car radio heading home to a hairdryer and somewhat less bedraggled attire for the count.

Yet here we are just a few days later, embarking on an election for leader of the Liberal Democrats.

I went to see Tim on Wednesday afternoon to tell him I thought he should definitely stay on, and I was excited at the prospect of putting myself forward to be Deputy Leader. I was stunned when he told me he would be resigning that evening.

Listening to Tim’s dignified statement, outlining the personal turmoil he felt during the election, I can’t fault him for deciding to step down, but I feel very sad that it came to this. Tim has done so much for our party. In the devastating aftermath of the 2015 election, to build a record membership and increase MPs by 50% in just 2 years is a massive achievement. Just as important, is that we now have our most diverse Parliamentary Party ever. We owe Tim a massive debt of gratitude.

Since his shock announcement, I have been overwhelmed by so many lovely messages from people I know, and from many members I have not yet met, encouraging me to stand for leader. I am touched and flattered that you look to me – and I am determined to play a key role in our party’s leadership.

Passions run high on this issue, and I hope the debate will unfold with respect and kindness on both sides. Whichever side of the debate we are on, we should acknowledge that our aim is the same – a party where every individual can feel supported and welcome, with many more elected representatives at all levels, reflecting the diversity of our society in all ways, and making a positive impact on our communities.

In 2001, I took to the conference platform in Bournemouth, summating an amendment to a similar motion, in much the same vein as this weekend’s amendment submitted by the East Midlands. Liberal Youth have also voiced their opposition to all-women shortlists. The group of us campaigning on this issue had t-shirts specially printed for the occasion, declaring “I am not a token woman. Say No to all-women shortlists.” Our amendment was successful, and the Gender Balance Task Force was formed, now the Campaign for Gender Balance.

Congratulations to all of the new Liberal Democrat Peers announced today. They will strengthen our existing excellent team in the Lords, fighting for a democratically elected second chamber while in the meantime using their power to provide a check on the government and its worrying assaults on the poor, on our civil liberties, and on the environment.

It’s also good to see recognition for those in our party who have served our communities and our country so well – Sir Vince Cable, Dame Annette Brooke, Ben Williams OBE and others.

What is depressing and wearily familiar, however, is the missing women.

But surely our Lords list is balanced? 5 out of the 11 nominations (45%) for the peerage go to women, which is progress I suppose – of the 40 people nominated to the Lords under Nick Clegg’s leadership, just 17 (43%) were women.

And 45% women wouldn’t be so bad if the existing Lords group was well-balanced, but of our 101 Peers, just 35% are women – so we’re still far from equality.

The Liberal Democrats have always felt like a family, and none more so than with the rallying round after the crushing election results this month. As the results unfolded, the texts and tweets began to arrive. I had to read them in small batches over the next few days: it’s often the words of kindness that bring the raw emotions to the surface the most.

On one level, the pain I felt was deeply personal – Duncan and I both lost our seats after 12 years of campaigning and service to our communities. Compounding this was the shared anguish of watching liberal giants like Vince and Simon defeated; transfixed by the TV in a sort of stunned post-count vigil with my campaign manager Katy Gordon as the new political reality dawned.

By Friday morning, I was reunited with Duncan and Andrew, whose excited “Mummy, mummy!” was the best possible antidote to the haze of sleep-deprived sadness. I turned on the radio to hear Nick’s resignation speech – taking responsibility with dignity, and reinforcing the need for our liberal values more than ever – and that was when the tears flowed freely down my cheeks.

In the final days of this Government Lib Dems are still delivering our agenda against the odds, and against Conservative obstruction.

Under the coalition government the gender pay gap had fallen to its lowest level, at just under 20% – but this is still 19.1% too high. Despite our high levels of women’s employment the UK has the 8th highest gender pay gap in the EU.

Not only is the gender pay gap socially wrong in modern society, but economically it’s nonsensical not to reward our most talented female employees properly. We should value the contribution of women and men in the workplace equally, so our goal has to be eliminating the pay gap completely.

As a Business Minister and Minister for Women, I have worked very hard to persuade my Coalition colleagues of the virtues of tough action to tackle this long-term inequality. Their traditional resistance makes it all the more remarkable that Nick Clegg has, in the last few weeks of our term, secured a government amendment that guarantees all large businesses will have to publish the difference between average pay for their male and female staff. So today (Tuesday) I will proudly vote for our party’s manifesto commitment – for large companies to publish the difference in average pay between male and female employees – to become law.